Rovers turned in an insipid display to miss out on an Wembley semi-final at the expense of Millwall on Wednesday night.
"Some of the fans probably think it's more important to beat Burnley than it was to win on Wednesday night, which is probably a bit difficult to take at times," said Appleton, who is the fifth man to select Blackburn's first XI during a turbulent season.
"But I understand the rivalry, the fierce rivalry. We respect that massively and we'll be giving it absolutely everything on Sunday to try and make sure that we go into the end of the season on a high."
Results on Saturday left Rovers three points above the relegation zone at kick-off and Appleton is calling for cool heads after seven winless matches.
"If you're not relaxed and you start panicking then that's when you are in trouble," he added.
"We're making sure that the players are in the same frame of mind. I don't want them panicking, I don't want anyone making them panic.
"At this time of the season, regardless of where you are, you only need to win two or three games and everything's hunky dory again.
"But you've got to get yourself in the right frame of mind for that and panicking is not the right frame of mind."